- Understanding Solid Objects
- Understanding Sketching Techniques
- 3.1 Technique of Lines
- 3.2 Sketching Straight Lines
- 3.3 Sketching Circles, Arcs, and Ellipses
- 3.4 Maintaining Proportions
- 3.5 One-View Drawings
- 3.6 Pictorial Sketching
- 3.7 Projection Methods
- 3.8 Axonometric Projection
- 3.9 Isometric Projection
- 3.10 Isometric Drawings
- 3.11 Making an Isometric Drawing
- 3.12 Offset Location Measurements
- 3.13 Hidden Lines and Centerlines
- 3.14 Angles in Isometric
- 3.15 Irregular Objects
- 3.16 Curves in Isometric
- 3.17 True Ellipses in Isometric
- 3.18 Orienting Ellipses in Isometric Drawings
- 3.19 Drawing Isometric Cylinders
- 3.20 Screw Threads in Isometric
- 3.21 Arcs in Isometric
- 3.22 spheres in Isometric
- 3.23 Oblique Sketches
- 3.24 Length of Receding Lines
- 3.25 Choice of Position in Oblique Drawings
- 3.26 Ellipses for Oblique Drawings
- 3.27 Angles in Oblique Projection
- 3.28 Sketching Assemblies
- 3.29 Sketching Perspectives
- 3.30 Curves and Circles in Perspective
- 3.31 Shading
- 3.32 Computer Graphics
- 3.33 Drawing on Drawing
- Key Words
- Chapter Summary
- Worksheets
- Review Questions
- Sketching Exercises
This chapter is from the book
This chapter is from the book
This chapter is from the book
3.18 Orienting Ellipses in Isometric Drawings
Figure 3.49 shows four-center ellipses constructed on the three visible faces of a cube. Note that all the diagonals are horizontal or at 60° with horizontal. Realizing this makes it easier to draw the shapes.
3.49 Four-Center Ellipses
Approximate ellipses such as these, constructed from four arcs, are accurate enough for most isometric drawings. The four-center method can be used only for ellipses in isometric planes. Earlier versions of CAD software, such as AutoCAD Release 10, used this method to create the approximate elliptical shapes available in the software. Current releases use an accurate ellipse.
STEP by STEP: DRAWING A FOUR-CENTER ELLIPSE
Draw or imagine a square enclosing the circle in the multiview drawing. Draw the isometric view of the square (an equilateral parallelogram with sides equal to the diameter of the circle).
Mark the midpoint of each line and draw a perpendicular line from each.
Draw the two large arcs, with radius R, from the intersections of the perpendiculars in the two closest corners of the parallelogram.
Draw the two small arcs, with radius r, from the intersections of the perpendiculars within the parallelogram, to complete the ellipse.
TIP
Here is a useful rule. The major axis of the ellipse is always at right angles to the centerline of the cylinder, and the minor axis is at right angles to the major axis and coincides with the centerline.
More Accurate Ellipses
The four-center ellipse deviates considerably from a true ellipse. As shown in Figure 3.50a, a four-center ellipse is somewhat shorter and “fatter” than a true ellipse. When the four-center ellipse is not accurate enough, you can use a closer approximation called the Orth four-center ellipse to produce a more accurate drawing.
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3.50 Inaccuracy of the Four-Center Ellipse
STEP by STEP: DRAWING AN ORTH FOUR-CENTER ELLIPSE
To create a more accurate approximate ellipse using the Orth method, follow the steps for these methods. The centerline method is convenient when starting from a hole or cylinder.
Centerline Method
Draw the isometric centerlines. From the center, draw a construction circle equal to the actual diameter of the hole or cylinder. The circle will intersect the centerlines at four points, A, B, C, and D.
From the two intersection points on one centerline, draw perpendiculars to the other centerline. Then draw perpendiculars from the two intersection points on the other centerline to the first centerline.
With the intersections of the perpendiculars as centers, draw two small arcs and two large arcs.
Enclosing-Rectangle Method
Locate center of circle and block in enclosing isometric rectangle.
Use the midpoint of the isometric rectangle (the distance from A to B) to locate the foci on the major axis.
Draw lines at 60° from horizontal through the foci (points C and D) to locate the center of the large arc R.
Draw the two large arcs R tangent to the isometric rectangle. Draw two small arcs r, using foci points C and D as centers, to complete the approximate ellipse.
Note that these steps are exactly the same as for the regular four-center ellipse, except for the use of the isometric centerlines instead of the enclosing parallelogram. (When sketching, it works fine to just draw the enclosing rectangle and sketch the arcs tangent to its sides.)
TIP: Isometric Templates
Special templates like this isometric template with angled lines and ellipses oriented in various isometric planes make it easy to draw isometric sketches. The ellipses are provided with markings to coincide with the isometric centerlines of the holes—a convenient feature in isometric drawing.
You can also draw ellipses using an ellipse template. Select the size and alignment of the major and minor axes of the ellipse to match the orientation of the shape in your drawing.
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